full scale investigation of bilge keel effectiveness at ... · the objective of this thesis is to...

Full Scale Investigation of Bilge Keel Effectiveness at Forward Speed

David James Grant

Thesis submitted to the Faculty of Virginia Polytechnic

Institute and State University in partial fulfillment of

the requirements for the degree of

MASTER OF SCIENCE in

Ocean Engineering

Dr. Leigh S. McCue, Chairman Dr. Owen F. Hughes

Dr. Ali Etebari

April 28, 2008 Blacksburg, VA

Keywords: Bilge Keel, Roll Damping, Full Scale

Full Scale Investigation of Bilge Keel Effectiveness at Forward Speed

David J Grant

ABSTRACT

Ship motions in a seaway have long been of great importance, and today with

advanced hull forms and higher speeds they are as important as ever. While one can now

often adequately predict heave, pitch, sway, yaw and even surge, roll motions are much

more difficult. Roll is the one motion that is very dependent upon viscous effects of the

fluid. Recently, at David Taylor Model Basin, there have been model experiments where

the bilge keels were instrumented in order to directly measure their damping force upon

the vessel. To build upon this work and to validate it when applied to full scale vessels, a

trial using the Italian naval vessel Nave Bettica was performed.

The objective of this thesis is to describe the experiment, present and analyze the

results, and offer some conclusions based upon these results. The process of

instrumenting the port bilge keel using strain gages and correlating their output to

pressures and total forces is described. Selected results for different forward speeds are

presented, with full results in the appendices. Particle image velocimetry (PIV) was also

performed during the test and was used to measure the flow field in a three foot by three

foot area under the aft end of the same bilge keel. Selected image series are presented, as

is a methodology for using these images to calculate the center of pressure and the

corresponding results.

ACKNOWLEDGEMENTS

I would like to express my sincere appreciation and gratitude to the following: Dr. Leigh McCue, my chairman, for accepting me as one of her graduate students, for helping me through the process of putting together a thesis, and for her continued support and feedback. Dr. Ali Etebari, my committee member, for his participation in this project and his help and guidance along the way. Dr. Owen Hughes, my committee member, for his support and feedback as well as his instruction during my time in graduate school. Allen Engle and Dr. Paisan Atsavapranee of NSWCCD for their participation in this project, as well as for getting me involved and supporting my efforts presented herein. Jason Carneal of NSWCCD for his work above, below, and within the ship during the test as well as his incredible attitude throughout. Scott Percival, Todd Beirne, James Herring, Jaime Corzo, and David Bochinski of NSWCCD for their participation in this project. Claudio Lugni of INSEAN and the Crew of the Bettica for all of their cooperation across the Atlantic and assistance during the setup and testing. Cailin, Marlee, and Emma Grant, my children, for constantly reminding me that, “Daddy has homework to do.” And finally my wife, Erin, for her continuous love, support, and friendly taunting throughout this process.

iii

TABLE OF CONTENTS

Chapter 1 Introduction 1

1.1 Background 1 1.2 Objectives 1 1.3 Nave Bettica 2

Chapter 2 Test Setup 4

2.1 Strain Gages 4 2.1.1 Design 4 2.1.2 Locations 6

2.1.3 Installation, Hookup, and Waterproofing 7 2.1.4 Data Collection 10 2.1.5 Calibration 10

2.2 Particle Image Velocimetry 13 2.2.1 PIV Camera 14 2.2.2 Laser Probes 14 2.2.3 Seeding 15 2.2.4 Calibration 16

Chapter 3 Test Procedure 17

3.1 Test Conditions 17 3.2 Zeroes 18 3.3 PIV Seeding 18 3.4 Forced Oscillation 18 3.5 Data Collection 19

Chapter 4 Analysis Procedure 20

4.1 Gage Calibration Values 20 4.2 FEA Model Verification 22 4.3 Bilge Keel Force 23 4.4 Data Processing 25 4.5 PIV Center of Pressure 28

Chapter 5 Results 31

5.1 Steady State Lifting Force 31 5.2 Roll Damping Results 33 5.3 Center of Pressure 42 5.4 PIV Images 43

iv

Chapter 6 Conclusions & Discussion 48

6.1 Bilge Keel Forces 48 6.2 Center of Pressure 50 6.3 Flow Field Measurement 51 6.4 Limitations of Current Work 51 6.5 Recommendations for Future Work 52

References 54 Appendix A Ship Characteristics 55 Appendix B Run Logs & Channel Zeros 60 Appendix C Complete Roll Damping Force Plots 65 Appendix D Additional PIV Image Series 98

v

LIST OF FIGURES Figure 1 Nave Bettica Outboard Profile 2

Figure 2 Outboard View of the FEA Model 4

Figure 3 Inboard View of the FEA Model 5

Figure 4 Bilge Keel Gage Longitudinal Locations 6

Figure 5 Bilge Keel Cross Section 7

Figure 6 Strain Gage Wiring Diagram 8

Figure 7 Installed Wireway 9

Figure 8 Installed Gages at Location 4 (BK4) 9

Figure 9 Calibration Setup 12

Figure 10 Calibration Output for Location 6 (BK6) 12

Figure 11 PIV Measurement Plane Location 13

Figure 12 Installed PIV Camera 14

Figure 13 Installed Laser Probes 15

Figure 14 Camera, Laser, and PIV Calibration Target 16

Figure 15 Shunt Calibration Diagram 20

Figure 16 FEA Analysis of 100 lbf Point Load at Location 3 (BK3) 23

Figure 17 FEA Analysis of 0.83 psi Distributed Pressure Load 24

Figure 18 Steady State Lift Forces 31

Figure 19 Steady State Individual Gage Pressures 32

Figure 20 Total Force at 0.0kts 33

Figure 21 Individual Gage Pressures at 0.0kts 33



Figure 24 Frequency Separated Forces at 5.0kts 35







vi







Figure 37 Pressure Contours in Negative Roll at 5.0kts 42

Figure 38 Pressure Distribution Across Bilge Keel Span 43

Figure 39 PIV Images at 5.0kts (t = 0,1,2,3,4,5s) 44




vii

LIST OF TABLES Table 1 Strain Gage Voltage Gain Values 21

Table 2 Pressure Gain Values 24

Table 3 Moment Gain Values 25

viii

CHAPTER 1 INTRODUCTION

1.1 Background

A collaborative effort between the United States Department of Defense and the

Italian Ministry of Defense has been underway for several years to develop a 6-degree of

freedom (DOF) Reynolds Averaged Navier-Stokes (RANS) model for ship maneuvering.

The goal of this effort is to improve the prediction of all 6-DOF motions of surface ships

operating in a seaway with particular emphasis on roll motions.

To date there has been significant effort at David Taylor Model Basin (DTMB)

addressing roll damping using computation and model testing methods. In particular, two

recent papers present methods for estimating bilge keel damping force using data from a

typical surface combatant model with instrumented bilge keels. Atsavapranee et al.

(OMAE 2007) present a method for a vessel undergoing roll-decay and Grant et al.

(OMAE 2007) expand upon this bilge keel force model and extend the method to include

coupled roll and heave motions in beam wave fields.

1.2 Objectives

This experiment was performed at varying forward speeds in calm water to obtain

a full scale data set for bilge keel forces and flow field measurement of a modern light

combatant hull form. The port bilge keel had strain gages installed at multiple locations

and the data analyzed to yield bending moments at each location. The strain gage output

was correlated to pressure values by assuming a uniform pressure distribution across the

bilge keel span. Since there are eight gage locations on the bilge keel, this yields pressure

distribution along its length. This is then integrated to give the total bilge keel force

acting on the vessel.

1

Particle image velocimetry (PIV) was used to record the flow field under the bilge

keel near its aft end within a three foot by three foot cross section. Processing these

images yield in-plane velocities. The full PIV data set can be used to validate

computational models and give flow visualization, clearly showing vortex formation and

shedding.

1.3 Nave Bettica

The Italian Naval Vessel Bettica (P-492) is a modern light combatant and the

third vessel in the Commandante class. The vessel’s overall length is 88.6m (291ft),

length at the design waterline is 80.0m (262ft) it has a maximum beam of 12.2m (40ft), a

full load displacement of 1520 metric tons (1496 long tons) and full load draft of 3.2m

(10.5ft). The outboard profile is shown in Figure 1. The body plan and curves of form

can be found in Appendix A.

Figure 1 – Nave Bettica Outboard Profile

The vessel is equipped with both active and passive roll damping measures. The

bilge keels begin approximately at midships and go aft 11m (36.1ft) with a span of

450mm (17.7in). The vessel also has active fins located 4.7m (15.4ft) forward of

midships (measuring to the pivot point). These active fins are 2.0m (6.6ft) long with an

average chord length of 1.9m (6.3ft). More information on the bilge keels can be found

2

in Chapter 2 and Appendix A, and more information on active fins can be found in

Appendix A.

The ship has two small boats that are stowed on the port and starboard sides

behind roll-up doors. During this experiment one of the boats was removed and the port

side boat room was used as a control room. The data collection systems, lasers, and seed

manifold were located here.

The Nave Bettica is based out of the naval arsenal in the city of Augusta, on the

island of Sicily. Installation of the equipment was performed in Augusta during a dry

dock period in August and September of 2007. The experiment commenced as soon as

the ship had left dry dock and refueled. The testing was performed on the east side of

Sicily at night.

3

CHAPTER 2 TEST SETUP

2.1 Strain Gages

The ship’s port bilge keel was instrumented along its length with the goal of

measuring the total force exerted on the hull.

2.1.1 Design

A finite element analysis using the expected pressure on the bilge keel was

performed to look at bending strain. The model included all main structural elements

from frame 42 to frame 75, and from the keel to the main deck. Figures 2 and 3 show the

FEA model, with the main deck removed for clarity. Note that initially the plan called

for the starboard side bilge keel to have the gages installed. Therefore the model was

constructed for this side. Due to ship symmetry port to starboard, the model was left as

the starboard side.

Figure 2 – Outboard View of the FEA Model

4

Figure 3 – Inboard View of the FEA Model

Strain was found to be maximum at locations where there was structure (frames,

bulkheads, etc) behind the line of bilge keel attachment inside the vessel. From the FEA

model it was anticipated that the strain seen at the gage locations would be very low,

approximately 50 microstrain. The cables to the gage locations would be up to 75 feet

long before reaching the amplifiers. The noise that might be seen from the vessel’s

machinery and electronics was a concern during the planning phase. Steps were taken to

maximize the signal to noise ratio, including 50 Hz filtering, shielded cable, etc.

It is possible to measure force directly using two gages separated along the

direction of measured strain by a known distance. The output of this method is the

difference in bending strain between the two gages. This value gets smaller as the gages

get closer. While not practical on this test, this method would typically be employed by

using a full Wheatstone bridge with two gages on each side of the member. This

5

effectively doubles the output since one side is in compression while the other is in

tension.

However, any force exerted on the member between the two gages will decrease

the accuracy, meaning that the gages should be placed very close to each other relative to

the overall span for pressure applications. In this case our signal would have been much

too small to measure and most likely lost in the anticipated noise. For this reason it was

decided to use a half bridge and only measure the bending moment at each location.

2.1.2 Locations

There were eight locations where framing intersected the bilge keel. These

locations became the locations for the eight gages and are shown below in Figure 4. Note

that the frame numbering starts at the aft end of the vessel. The gages were placed at one

inch from the plate attaching the bilge keel to the hull. See Figure 5 for bilge keel cross

section dimensions.

Figure 4 – Bilge Keel Gage Longitudinal Locations

6

Figure 5 – Bilge Keel Cross Section

In addition to the eight locations on the bilge keel, a 9th gage set was installed on

an unattached piece of 8mm steel. This was left in the cable tray above the bilge keel and

was designed as a reference gage to correct for temperature changes during testing and

any other strain offsets that might occur when the ship was re-floated after the

drydocking period.

2.1.3 Installation, Hookup, and Waterproofing

The installed design used two linear 350 ohm gages (Vishay CEA-06-W-250A-

350) to form a half bridge. Three wires were run to each gage, and precision dummy

resistors were used prior to the amplifiers to complete the Wheatstone bridge (Figure 6).

Vishay model 2310 amplifiers were used. Excitation voltage to each gage was measured

and recorded coming from the amplifier, but was nominally 10 volts. The amplifier gain

was set to 1000, and the amplifiers were adjusted to balance the bridge prior to testing.

7

Figure 6 – Strain Gage Wiring Diagram

The cable used was water-blocked 22 AWG, with three shielded pair (Monroe

Cable LS2SWAU-3). The cables were run from the amplifiers in the port boat room,

down the hull, and aft along the top of the bilge keel in a removable stainless steel

wireway installed for this test. Figure 7 shows the installed wireway as it turns aft along

the top of the port bilge keel and Figure 8 shows the installed gages at location four

(BK4).

8

Figure 7 – Installed Wireway

Figure 8 – Installed Gages at Location 4 (BK4)

9

2.1.4 Data Collection

With the exception of PIV images, all data channels were collected at 20 hertz

using a PC in the control room running LabView. This computer recorded the bilge keel

strain, ship motions, GPS speed and direction, and PIV synchronization signals. Nine

channels from the bilge keel amplifiers and the synchronization signal were aquired using

a National Instruments analogue to digital converter. A Garmin GPS unit was used for

speed over ground and heading. Latitude and longitude were also recorded throughout

the test. The PIV system was manually triggered for each run and a 5V synchronization

pulse was recorded on an analogue channel.

All six components of ship motion were measured using a LN200 fiberoptic gyro.

This gyro was aligned so that the positive X axis pointed forward, the positive Y axis

pointed to starboard, and positive Z was pointed down. This means that positive roll was

starboard down. The gyro was physically mounted on top of the bridge overhead at

frame 68. The GPS antenna was also mounted at this location.

Ship speed through water, heading, water temperature, wind speed and direction

were to be measured using the ship’s instrumentation. They were noted for each run and

manually recorded in the run log. Initial planning included the use of a new wave radar

being installed on the ship at the same time. However, this radar was not operational by

the beginning of testing and so significant wave height was estimated by the ship’s crew

from the bridge and recorded manually.

2.1.5 Calibration

There were two calibrations performed on the installed gages and acquisition

system. The first was a shunt calibration. A shunt resistor of 846,000 ohms was applied

10

across each gage and the output voltage recorded. The resistance was sized to mimic 100

microstrain and therefore an output of approximately one volt at a gain of 1000. This

calibration was recorded as Run 21.

The second calibration involved directly loading the bilge keel and recording the

output. At each gage location, the bilge keel was loaded in both the up and down

direction. Due to the geometry within the drydock, it was not possible to apply the load

perfectly perpendicular to the bilge keel. Instead, the loads in the up direction were

applied at 30 degrees from the ship’s center plane and the loads in the down direction at

240 degrees from the center plane. The average angle of the bilge keel is 148 degrees,

although it changes slightly along its length.

The load was applied using free weights hung from a line and re-directed through

one pulley in the up direction and two pulleys when in the down direction. Due to

friction and hysteresis in this system, a load cell was used to measure the actual applied

force on the bilge keel at the point of application. Six empty compressed air tanks were

used as weights. They were added and removed incrementally and a run recorded each

time. Including the zero runs, this yielded 13 calibration points in each direction at each

gage location. These were recorded as runs 40 to 251. Figure 9 shows the calibration

setup and Figure 10 shows a sample of the calibration output.

11

Figure 9 – Calibration Setup Load cell output shown on the left, weights on the right.

BK 6 cal

y = 0.0032x - 0.1826R2 = 0.9992

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

-20 0 20 40 60 80 100 120 140 160 180

Force (lbf)

Out

put (

volts

)

Figure 10 – Calibration Output for Location 6 (BK6)

12

2.2 Particle Image Velocimetry

PIV is a standard in global flow-field measurements. With one camera it is

possible to get in-plane velocity measurements of a planar cross-section of flow. Using

two cameras in a stereo configuration will yield all three velocity components and is

referred to as stereo particle image velocimetry (SPIV). While initial plans called for

using SPIV on this test, it was decided to simplify to one camera to help mitigate risk and

reduce costs. The location of the PIV measurement plane is shown in Figure 11.

Figure 11 – PIV Measurement Plane Location

The PIV technique uses seed particles in the fluid as tracers. These particles are

ideally very small (micron-sized) and neutrally buoyant. A laser sheet from a high-

powered laser is used to illuminate these particles within a thin section of the flow field

with two consecutive pulses separated by a very small Δt. The Δt was varied according

to ship speed and recorded in the run log. A high speed camera is used to record this

image pair. Then a statistical cross-correlation is performed between square subsets of

the two images, essentially tracking the movement of the tracer particles and yielding the

velocity vectors.

13

2.2.1 PIV Camera

The camera (Redlake ES 4.0, 2048 x 2048 pixels) was used in dual exposure

mode at a frame rate of 6 fps. The camera was mounted in a custom waterproof

enclosure with a 30m (100ft) umbilical that used the same cable tray as the strain gauges.

The camera was mounted approximately two feet off the hull directly aft of the target

area on a stainless steel v-strut. The camera had full adjustment in roll and slight

adjustment in yaw and pitch. The camera was focused remotely during the calibration

procedure. Figure 12 shows the installed camera.

Figure 12 – Installed PIV Camera

2.2.2 Laser Probes

Two flash lamp, pumped dye lasers (modified Cynosure V-Star, 585 nm, 1 J/pulse

maximum) were used to form the light sheet in 10 microsecond pulses at 6 hertz. The

laser was coupled into optical fibers and formed into sheets using beam-forming optics in

submersible housings. Both lasers were used in tandem to illuminate the maximum

14

possible target area. The laser optic housings were mounted to a stainless steel v-strut

similar to the camera and inboard of the target area. Figure 13 shows the installed laser

probes.

Figure 13 – Installed Laser Probes

2.2.3 Seeding

In order to ensure that there would be enough reflective particulate in the water

for good PIV images, a particle seeding system was installed. The chosen seeding

material was diatomaceous earth. While not completely neutrally buoyant, it was found

to be effective in preliminary tests for this kind of application. This was mixed into

slurry and pumped to a three inch venturi-type mixing nozzle, where it was further

diluted with seawater.

The main source of water came from two hydrants on the ship’s fire main. The

final seed mixture was then sent through a manifold to be dispersed from four seed pipes

running down the side of the hull. The seed pipes were staggered so that they would

form four zones running from the water line to the keel. The manifold used

pneumatically controlled three-way valves to direct the seed mixture to the correct zones

to get optimal seed placement downstream at the target area.

15

It was found that the seeding system was only required for the lower speed runs

during testing. Higher speed runs achieved larger roll angles and the extra turbulence

seemed to bring more of the natural surface particulate into the target area.

2.2.4 Calibration

A 36 inch by 36 inch precision calibration target was mounted to the hull and then

aligned to the laser sheet. The dry dock was partially submerged in order to immerse the

bilge keel and target area. A diver was used to make final adjustments to the camera

angles and laser optics. The target was then illuminated and a series of calibration

pictures were recorded. Once a satisfactory calibration was obtained, the dry dock was

brought back to its normal position and the target was removed. A picture of the target

and calibration setup can be seen in Figure 14.

Figure 14 – Camera, Laser, and PIV Calibration Target

16

CHAPTER 3 TEST PROCEDURE

3.1 Test Conditions

The testing was performed on the nights of October 4th, 5th, 8th, 9th, and 10th, 2007

(referred to as days one through five) in the Mediterranean, off the east coast of Sicily.

While the test was designed as a calm water test, completely calm water is very rare for a

full scale trial. The first night of testing was used mainly to troubleshoot the system, and

the conditions were very favorable with very light winds and ambient waves. The second

night of testing also proved to be very favorable, again with very light winds and ambient

waves. There was storm during the weekend before testing recommenced on day three.

Days three through five had moderate wind and more significant ambient waves than

days one and two as the remnants of the storm lingered.

Ship speed through water was set by the crew to the specified value and measured

by the vessel’s equipment. Ship speed over ground and ship direction were recorded

directly from the GPS antenna by the data collection system. Water temperature, wind

speed and direction were manually entered in the run log from the vessel’s equipment.

The significant wave height was estimated by the ships’ crew on days three, four, and

five and manually recorded in the run log. The run log can be found in Appendix B.

The ship generally held to a course that provided either 0 or 180 degree angle of

encounter with the ambient wave field as it traversed back and forth through during each

night’s testing. Wind speeds varied from 0 to maximum of 18 knots. Estimated

significant wave heights varied from 0 to 25 centimeters (0-10in).

17

3.2 Zeroes

Throughout each night of testing zeroes were taken at least every six damping

runs. The ship would come to a zero speed through water, and zeros would be collected

by the acquisition system. Then a run would be recorded with the ship still at zero speed.

The ship would then accelerate to the designated test speed. A steady-state run with the

active fins in automatic mode would be taken before damping runs commenced.

3.3 PIV Seeding

When collecting PIV runs it was evaluated whether seed would be needed. The

higher speed runs did not seem to need the seed, while the 5 and 7.5 knot runs did.

Higher speed runs achieved larger roll angles and the extra turbulence seemed to bring

more of the natural surface particulate into the target area. The seed slurry was kept

mixed in the starboard boat room. Prior to the beginning the run, water to the three inch

mixing nozzle was turned on by the ship’s crew. Slurry was then pumped to the mixing

nozzle for the duration of the run. The three way valves were initially adjusted for

optimum seed placement and did not need to be actively adjusted during the roll cycle as

originally planned.

3.4 Forced Oscillation

To excite the vessel in roll the ship’s crew would manually actuate the active fins

at the natural roll frequency of approximately 9-10 seconds. When it appeared the

maximum roll angle had been achieved the fins would be released back to the zero

position. The point of release in seconds was recorded for each run.

18

3.5 Data Collection

Data collection for each run was started when the forced oscillations started.

When used, the PIV system was started after the data collection system and a

synchronization trigger was recorded by the data collection computer. 2000 frames (167

seconds) of PIV data was taken for roll decay runs and 1000 frames (83 seconds) for

steady state runs. 200 seconds of data was taken by the data collection system when the

PIV system was being used, and 100 seconds when there was no PIV.

19

CHAPTER 4 ANALYSIS PROCEDURE

4.1 Gage Calibration Values

The shunt resistor calibration was performed for each gage as described in

Chapter 2. Data was collected for four to five seconds for each of the 18 individual

gages. The values for each gage were averaged and the standard deviation calculated.

The absolute average values of the two gages at each location were averaged to give a

single value for each of the 9 gage locations. These values give a voltage output for a

known change in gage resistance.

Referring back to Figure 6, it can be seen that this 846,000 ohms of added

resistance is placed across the gage and the resistance in the wires down and back.

Therefore the resistance of the wire needs to be included and is calculated based on wire

gauge and length. The 22 awg wire used has a resistance of 0.01614 ohms/ft. The

change in gage resistance can be found by evaluating the simple resistor circuit shown

below in Figure 15.

Figure 15 – Shunt Calibration Diagram

20

11

21

−

⎟⎟⎠

⎞⎜⎜⎝

⎛+

+=

SHUNTWIREGAGETOTAL RRR

R

TOTALWIREGAGEGAGE RRRR −+=Δ 2

For this experiment the gage resistance was 350.0 ohms and the wire resistance

was calculated for each gage location. With the change in resistance of the gage we can

calculate the strain using the basic equation for gain factor:

fGRR /Δ

=ε

where ε is strain and Gf is the gage factor of the installed strain gage. The manufacturer

listed the gage factor for this lot of gages at 2.06. While the shunt resistor was applied

across a single gage, this installation used a half bridge with two gages measuring the

same strain. Therefore the output signal for actual strain is doubled and our equation

becomes:

fGRR /

21 Δ

=ε

Calibration values for obtaining strain per volt recorded are then calculated and can be

seen tabulated below in Table 1.

Excitation RWIRE ΔRGAGE Output Gain Gage Location volts ohms ohms

Apparent Strain volts strain/volt

BK1 9.94 0.7263 0.1459 1.012E-04 1.034 9.791E-05 BK2 9.96 0.82314 0.1461 1.013E-04 1.033 9.810E-05 BK3 9.97 0.91998 0.1463 1.014E-04 1.045 9.705E-05 BK4 9.98 1.01682 0.1464 1.015E-04 1.042 9.749E-05 BK5 9.96 1.0491 0.1465 1.016E-04 1.037 9.797E-05 BK6 9.97 1.08138 0.1465 1.016E-04 1.036 9.811E-05 BK7 9.97 1.11366 0.1466 1.017E-04 1.030 9.871E-05 BK8 9.97 1.2105 0.1467 1.018E-04 1.038 9.809E-05 BK9 9.96 0.91998 0.1463 1.014E-04 1.037 9.778E-05

Table 1 – Strain Gage Voltage Gain Values

21

4.2 FEA Model Verification

The FEA model examined during the experiment planning showed that strain

would be maximum where the bilge keel was rigidly constrained, i.e. at the frame and

bulkhead locations. For a given pressure, the strain between the supporting structure was

much lower. Therefore it was decided to use the FEA model to correlate the measured

strain values to a pressure load.

Rarely are large FEA models perfect, especially when looking at very localized

strains such as seen at the gage locations. Ideally a calibration would have been

performed on the bilge keel using a known distributed load that was representative of the

loads that would be seen during vessel rolling. Since this was not feasible while in dry

dock, point load calibrations were performed as described in Chapter 2.

The first thing was to check the model against the measured strain values from the

point load calibrations. The point load calibrations yielded volt per load values and the

shunt calibrations yielded the strain at each gage. The corresponding strain at 100 lbf

was then calculated at each location for the up and down directions.

The 100 lbf point loads were applied to the FEA model and the strain at each gage

location tabulated. Figure 16 shows the FEA results from one of these load cases. The

point calibrations in the down direction were closer to perpendicular to the bilge keel and

therefore these were the values used for comparison to the calibration. The FEA model

over-predicted the strain, as is typical of coarse-mesh models. This is most likely

explained by the lack of detail where the gages are and differences between the ideal

model and the actual gage installation aboard the vessel. However, it is still reasonable to

22

assume that the relative strain distribution along the bilge keel would be would be

accurate.

Figure 16 – FEA Analysis of 100 lbf Point Load at Location 3 ( BK3 )

4.3 Bilge Keel Force

Using this assumption the FEA model was loaded with a uniform pressure until

the strain values were approximately 100 microstrain (0.83 psi). The FEA results are

shown in Figure 17. Reducing these strain values by the differences in the point

calibration for each gage location allows us to calculate a pressure gain, or applied

pressure per strain at a gage. The results can be seen below in Table 2.

23

Calibration 100lbf FEA 100lbf FEA

0.83psi Actual 0.83psi

Pressure Gain Gage

Location Strain Strain

DifferenceStrain Strain psi/Strain

BK1 4.422E-05 8.054E-05 82% 6.517E-05 3.578E-05 2.320E+04 BK2 3.155E-05 5.160E-05 64% 1.056E-04 6.457E-05 1.285E+04 BK3 3.463E-05 5.214E-05 51% 1.092E-04 7.252E-05 1.145E+04 BK4 3.437E-05 5.056E-05 47% 1.006E-04 6.838E-05 1.214E+04 BK5 2.810E-05 4.838E-05 72% 9.237E-05 5.366E-05 1.547E+04 BK6 3.114E-05 4.837E-05 55% 9.183E-05 5.912E-05 1.404E+04 BK7 3.275E-05 5.054E-05 54% 9.882E-05 6.404E-05 1.296E+04 BK8 4.058E-05 5.999E-05 48% 9.544E-05 6.456E-05 1.286E+04

Table 2 – Pressure Gain Values

Figure 17 – FEA Analysis of 0.83psi Distributed Pressure Load

The total force on the bilge keel can be calculated by integrating the pressure

distribution along its length. Trapezoidal integration was used. Since the first and last

gages are not at the extreme ends of the bilge keel, the pressures at those gages will be

assumed to extend to their respective extreme ends. Because there is unequal gage

spacing the equation can be written as:

24

83876543212

11 34

32

32

3422

2PAPPPPPPPPAPAFTOTAL +⎟

⎠⎞

⎜⎝⎛ ++++++++=

where P1, P2, … , P8 are the pressures at each location and A1 is the area forward of the

first gage (251in2), A2 is the area between every three frames (1233in2), and A3 is the area

aft of the last gage (594in2).

Since the gages are actually measuring bending moment at their location, the

center of pressure is required to calculate the actual force on the bilge keel if the pressure

is not uniform. So far it has been assumed that the pressure was evenly distributed,

therefore the center of pressure is located midway between the gage and the bilge keel

tip. It is desirable to be able to have a set of gains that give the bending moment as

function of recorded voltage. This allows refined center of pressure numbers to be used

to calculate overall bilge keel force. These gains are shown below in Table 3.

Moment Gain Gage

Locationin-lb/volt

BK1 3.055E+02BK2 1.696E+02BK3 1.494E+02BK4 1.592E+02BK5 2.038E+02BK6 1.853E+02BK7 1.721E+02BK8 1.696E+02

Table 3 – Moment Gain Values

4.4 Data Processing

Strain gage and gyro data were recorded in comma delimited (.csv) files during

the experiment. Processing of this data and most of the plotting was completed using

MATLAB. Some of the MATLAB output was compiled in Excel for plotting. PIV

25

image pairs were processed using the software DaVis, and the resulting vector fields

plotted using TecPlot 360.

To start, the run log and the zeros for each channel were examined to determine

which runs would be useful. Unfortunately, the strain gage amplifiers were not powered

on the first day of testing, leaving no strain gage data for those runs. Additionally, runs

271, 294, and 330-334 were excluded due to bad zeros. This left 63 roll damping runs

and 34 steady state runs, including 6 zero-speed runs.

All the gages were zeroed frequently during each night’s testing, including the

reference gage, BK9. As a result, the values recorded from BK9 were relatively low.

However the data from BK9 for each run was averaged and subtracted from the other

eight channels as a steady state offset.

Steady state runs were compiled into a mean value for each run and combined

into plots showing lift as a function of forward speed. In addition to the total force, the

individual pressures at each gage location were plotted in order to show distribution

along the length of the bilge keel.

Within the body of this thesis, one representative roll damping run at each

forward speed is presented and examined in depth. Additionally, one zero run is looked

at for roll damping comparison. Total force, roll angle, and tangential velocity at the

bilge keel tip are presented for all roll damping runs in Appendix C.

Data was initially analyzed starting when the active fin was released back to zero

by the helmsman. However, transients from the fin took one to three seconds to pass

over the bilge keel. Therefore the starting point for each run became the release point

plus three seconds. Thirty seconds, or approximately the time required for three roll

26

cycles, was analyzed. After this the rolling had decayed into a steady state condition.

Total force and individual gage pressures were plotted for this sample period.

It became apparent that some of the components of the force on the bilge keel

were not varying at the same frequency as the ship’s roll. Therefore a Fourier analysis

was performed and the first, second, and third harmonics were reconstructed and plotted.

The spectral content of the force signal can be computed by performing a Fourier

analysis on the force signal. The Fourier Series representation of a signal f(t) is given by

the following equations, where f(t) is the signal to be represented, t is time, ai are the

cosine term coefficients, bi are the sin term coefficients, and T is the period over which

the representation is performed. For this experiment, T was selected as the time between

the nth and 2 + nth roll zero crossings for cycle number n. Since the ship had a steady list

to port, the mean roll amplitude over the entire run was subtracted from the signal to

ensure the zero crossings detected were referenced to a change from the steady state

condition.

∑=

++=n

iiin tnbtna

atf

1

0 )sin()cos(2

)( ωω

∫=T

i dttktfT

a0

)cos()(2 ω

∫=T

i dttktfT

b0

)sin()(2 ω

In order to calculate the Fourier coefficients ai and bi for the force signal, the Fast Fourier

Transform (FFT) was used in MATLAB. The coefficients ai are the real portion of the

FFT coefficients, and the bi coefficients are the imaginary portion. To determine the

frequency content of the signals, the Power Spectral Density (PSD) of the signals was

27

calculated by multiplying the FFT coefficients with their complex conjugate. The

equations for the FFT X(fi) of a signal x(k) and a filtered signal y(k) are given below.

Y(fi) is the FFT of the filtered signal y(k), fi is frequency, and T is the uniform interval of

the signal, and F is the inverse of T.

∑∞

−∞=

−=k

kTfji

iekxfX )2()()( π

)()()( iii fXfHfY =

∫−−=

2/

2/

)2()(1)(F

F

kTfji dfefY

Fky iπ

4.5 PIV Center of Pressure

Up to this point, a uniform pressure distribution has been assumed for bilge keel

across its span. The center of pressure for a uniform load is the middle of that span. The

distance from this point to the gage center is the moment arm used to calculate force on

the bilge keel from the actual measured moment as discussed in above. Improving upon

this estimation of center of pressure would enable a similar improvement in the total

force calculation for the bilge keel.

The processed PIV images yield the in-plane velocities within the target area.

Knowing these u and v velocity components allows an approximate calculation of

relative pressures due to the ship’s rolling motions. To do this the Navier-Stokes

equations are written with the pressure gradient term on the left side and the acceleration

and viscous terms are left on the right hand side:

)()( 2uuutuP rrrr

∇+∇⋅+∂∂

−=∇ μρ

28

where P is pressure, ρ is the fluid density, the vector u is velocity, and μ is the fluid

viscosity. The pressure difference between any two points can be calculated as the line

integral between them. The individual components of the equation are given below:

wvuu ,,=r

tw

tv

tu

tu

∂∂

∂∂

∂∂

=∂∂ ,,r

zw

yv

xuu

∂∂

∂∂

∂∂

=∇ ,,r

zww

yvv

xuuuu

∂∂

∂∂

∂∂

=∇⋅ ,,rr

2

2

2

2

2

22 ,,

zw

yv

xuu

∂∂

∂∂

∂∂

=∇r

2

2

2

2

2

2

,,,,,,zw

yv

xu

zww

yvv

xuu

tw

tv

tuP

∂∂

∂∂

∂∂

+∂∂

∂∂

∂∂

−∂∂

∂∂

∂∂

−=∇ μρρ

For the present case, the out-of-plane component of the velocity, w, is assumed to

be constant in the z direction, and the unsteady acceleration terms are ignored. This gives

us the pressure gradient described by the following equation:

2

2

2

2

,,yv

xu

yvv

xuuP

∂∂

∂∂

+∂∂

∂∂

−=∇ μρ

A complete calculation of the pressures would also need to include the ambient

pressure, P0. While this is impossible determine from what we have, some improved

center of pressure estimate can still be performed. The desired value is a center of

pressure, which will depend upon the relative and not absolute magnitudes of the

pressures across the span, making P0 unnecessary.

29

For each of the five forward speed roll damping cases examined, the velocity

fields from the PIV images were processed in MATLAB. Line integrals were performed

in both the x and y directions and averaged, with the pressures normalized to the pressure

at the intersection of the hull and bilge keel to yield the pressures in the test plane.

Pressure values along the line of the bilge keel were then extracted from the processed

image and exported to Excel. Only images of the lower side of the bilge keel are

available. Pressures along the bilge keel were taken from images with velocities in both

directions of roll and compared. The resulting pressure profile for each side of the bilge

keel was plotted across the span, with the pressures at the tip set to zero to give a

common value at that point.

30

CHAPTER 5 RESULTS

5.1 Steady State Lifting Force

The average total lift force on the port bilge keel for each steady state run can be

seen plotted in Figure 18. Note that ship motions were measured with positive Z in the

down direction and positive roll was starboard down. Keeping consistent with this, the

lift is plotted with positive being aligned with the Z axis and therefore negative lift is

actually in the up direction.

Steady State Lift Forces

y = -6.4819x2 - 49.191x - 21.54R2 = 0.6315

-3000

-2500

-2000

-1500

-1000

-500

0

500

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0

Forward Speed (kts)

Lift

(lbf)

Posi

tive

Dow

n

Figure 18 – Steady State Lift Forces

The scatter in the data seems to derive from the scatter in the zero values collected

for each channel. However, when outlying zeros and corresponding runs were excluded,

the quadratic fitted through the data changed very little, with only the r-squared value

improving. With no better reason to exclude these runs, they have been left in the data

set plotted. 31

To obtain an idea of the pressure or lift distribution along the length of the bilge

keel, the individual pressures at each gage location were plotted and quadratics fit

through each set of points. This can be found below in Figure 19. Note that most of the

increase in lift due to forward speed happens at the leading edge. This is seen later in the

roll damping data as well.

Individual Gage Pressures

BK1 = -0.0034x2 - 0.0201x - 0.0299BK2 = -0.0007x2 - 0.0132x - 0.0147

BK3 = -7E-05x2 - 0.0129x - 0.0014

BK8 = -0.0005x2 - 0.0013x + 0.0052

BK7 = 4E-05x2 - 0.0073x - 0.0036

BK6 = -0.0012x2 + 0.0004x + 0.0046

BK5 = -0.0004x2 - 0.0048x - 1E-04

BK4 = -0.0004x2 - 0.0052x + 0.0012

-1.4000

-1.2000

-1.0000

-0.8000

-0.6000

-0.4000

-0.2000

0.0000

0.2000

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0

Forward Speed (kts)

Pres

sure

(psi

)

BK1BK2BK3BK4BK5BK6BK7BK8Poly. (BK1)Poly. (BK2)Poly. (BK3)Poly. (BK8)Poly. (BK7)Poly. (BK6)Poly. (BK5)Poly. (BK4)

Figure 19 – Steady State Individual Gage Pressures

32

5.2 Roll Damping Results

Figure 20 – Total Force at 0.0kts

Figure 21 – Individual Gage Pressures at 0.0kts

33



34

Figure 24 – Frequency Separated Forces at 5.0kts


35



36



37



38



39

Figure 34 – Total Force at 15kts


40

Figure 36 – Frequency Separated Forces at 15kts

41

5.3 Center of Pressure

Figure 37 shows a negative roll image (pressure side) for 5 knots during run 291

(Frame 53). The hull of the ship is shown at the top of the image, and the bilge keel is

shown at the left side. Figure 38 shows the relative pressures along both sides of the

bilge keel. The pressures were independently normalized to a magnitude of one and set

to a P0 at the tip where they should be the same value. Suction side pressures are

obtained by looking at a positive roll image (Frame 22) at a similar roll velocity. Since

the assumed P0 for each frame is different, they cannot be directly summed to give the

total pressure and are instead normalized to the maximum pressure for each frame.

Figure 37 – Pressure Contours in Negative Roll at 5.0kts

42

Center of Pressure - 5kts (Run 291)

-1.000

-0.500

0.000

0.500

1.000

1.500

2.000

0 50 100 150 200 250 300 350 400 450 500

Distance From Hull (mm)

Non

-Dim

ensi

onal

Pre

ssur

e

Pressure Side PressureSuction Side Pressure

Figure 38 – Pressure Distribution Across Bilge Keel Span

5.4 PIV Images PIV images are shown here for 5.0 (Run 291) and 10.0kts (Run 281). Every 6th

frame is shown, corresponding to one frame per second. Contours show vorticity, vectors

show the local velocity, and streamlines are also included.

43

Figure 39 – PIV Images at 5.0kts (t = 0,1,2,3,4,5s)

44


45


46


47

CHAPTER 6 CONCLUSIONS & DISCUSSION

6.1 Bilge Keel Forces

In two dimensional roll, the force on the bilge keel can be separated into viscous

and added mass components. The drag force due to viscous effects is at a maximum

when the roll velocity peaks, or as the ship rolls through its equilibrium position. The

added mass will reach a maximum value when roll acceleration is greatest or as the ship

reaches maximum roll amplitude. When forward speed is introduced, a third component

due to lift must also be considered. If the bilge keel is aligned to the steady state flow

along the hull, the lift term will be zero at even heel and vary as the flow around hull

changes with roll angle. Generally there is also a steady lift offset as the bilge keel is not

aligned to the flow at every, or sometimes any, forward speed. The coefficients for these

three force terms can be written as:

⎟⎟⎠

⎞⎜⎜⎝

⎛+++=

⎟⎟⎠

⎞⎜⎜⎝

⎛+++−=

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

∞

K

K

)cos()2cos(

4)cos(2

)sin()3sin(

)sin()2sin(4

21

321

0

2

tt

aaU

DCt

C

tt

btt

bbDU

C

aUU

C

m

mD

mm

mL

ωωαπ

ω

ωω

ωω

ωπ

The bilge keels on this vessel were not aligned to the flow around the hull, and the

steady state lift can be seen to increase with the square of forward speed in Figure 18.

Looking at the pressure distribution along the hull in Figure 19, the greatest lift forces are

occurring at the leading edge of the bilge keel. The flow appears to be hitting this leading

edge with significant angle of attack which diminishes as the flow aligns itself with the

bilge keel as it proceeds aft.

48

The steady state lift can also be seen in the roll decay runs, with the total force

developing an offset in the up direction (negative z). Individual pressure plots for the roll

decay runs also show the greatest lifting forces at the leading edge. However, unlike the

steady state runs there is often a corrective downward force at the trailing edge.

The total force in the zero speed plot (Figure 20) gives some insight as to what

was occurring while zeros were collected. There is some small roll motion due to the test

conditions. It would make sense that any roll at zero speed might yield more sinusoidal

force data on the bilge. It should be noted that the even while at zero speed, the ship’s

controllable pitch propellers did not stop rotating. Additionally the ship’s crew was

making use of the propellers to try and maintain heading at zero speed, causing water

movement around the aft end of the ship even when technically at zero speed. It can be

seen that the aft end of the bilge keel at BK8 did see higher pressures than the rest of the

gages by looking at Figure 21.

Forward speed roll damping runs do not show sinusoidal force response at the roll

frequency as was originally expected, especially at lower roll amplitudes. However,

there does seem to be some correlation for the first one to two roll decay cycles up to

12.5kts. During these periods the total force slightly leads the roll velocity. This trend

does break down once the roll amplitude has diminished below approximately plus and

minus three degrees, and above 12.5kts.

During the length of the runs it is evident that other frequencies seem to be

superimposed on the total force. Breaking out the different harmonics in the frequency

separated plots allows one to correlate this to other phenomena. Bilge keel natural

frequency was calculated and shown to be orders of magnitude above the frequencies of

49

interest. Frequency of vortex shedding based on Strouhal number was also calculated

using the following equation:

VnDS =

where n is the frequency, V is the free stream velocity, D is the diameter, and S is the

Strouhal number. This is based upon cylinders, but for foils the value of D can be

approximated as 0.26tmax. At Reynolds numbers above 103, the S remains constant at

0.21. The resulting frequencies range from 7Hz at 5kts to 20Hz at 15kts and are therefore

not the cause of the oscillations.

Runs taken during the last three days when ambient waves were more significant

show this trend more clearly. Without wave data it can only be conjectured that these

higher order frequencies correspond with wave encounter frequencies. An attempt was

made to group runs by day and heading to investigate whether an obvious frequency shift

could be found that might correspond to head or following seas. There is a difference in

these higher frequencies between different days, and also between the opposite directions

within the same day. This suggests that the ambient wave field is having an effect on the

bilge keel forces, but is difficult if not impossible to account for without more

information on the wave field or matching starboard force measurements.

6.2 Center of Pressure

During the processing of different runs for center of pressure, several things

became apparent. First, while an actual P0 is not necessary to calculate the center of

pressure on the bilge keel, the full pressure profile around the bilge keel using the same

assumed P0 is required. Since flow field data is only taken on one side of the bilge keel,

the best estimate can only be made by comparing an image with opposite roll direction

50

and equal velocity magnitude and roll angle. Since roll is decaying during the run, such

an image is not available.

Additionally, looking at the velocity fields in the PIV images makes it apparent

that the out of plane velocities cannot be ignored. Since they are unknown for this data

set, realistic centers of pressure cannot be obtained. Looking at the pressure gradient

along the bilge keel throughout the roll cycle did show that is possible to have the

pressure change from positive to negative along the span. This effectively will yield a

smaller force on the bilge keel while increasing the moment, causing erroneous force

values with the gage configuration used during this experiment.

6.3 Flow Field Measurement

The bilge keel force data suggest transients, mainly in the flow coming into the

bilge keel. This is evident when evaluating the PIV images as repeatable flow structures

are difficult to find, especially at the lower roll amplitudes. This is more pronounced at

higher forward speeds, especially at 15 knots, where much of the bilge keel and

measurement plane are within the boundary layer of the hull.

6.4 Limitations of Current Work

While designed as a calm water experiment, small waves were encountered.

These waves were larger on the last three days of testing and it appears that they have an

effect on the data – both for force and flow field. However, since detailed wave data was

not recorded during this test, correlating with the results directly is not possible, nor are

any corrections that might have been made to account for this.

The forces on the bilge keel were not directly measured. Instead, the gage

configuration allows only the measurement of bending moment at the gage location. The

51

force data presented in this paper is based on a uniform pressure distribution assumption.

Based on the center of pressure analysis, this assumption is not accurate. When the

pressures on both sides of the bilge keel are looked at together, it is possible that there

will be an effective pure moment in addition to the moment due to net force on the bilge

keel. This results in a large apparent force that has no effect on actual vessel roll

damping.

The Nave Bettica has a large active fin directly forward of the bilge keel. Even

though the fin was at not active during the roll decay, this would obviously have a large

effect on the flow into the bilge keel area. As the bilge keel rolls to port, the angle of

attack increases with roll velocity and the wake of the active fin will pass above the bilge

keel. As the roll velocity crosses zero and reverses, the angle of attack also reverses

causing the wake of the active fin to pass under the bilge keel. As a result, twice during

the roll cycle the wake from the active fin passes over the bilge keel and affects the forces

along the bilge keel and the total moment measured.

6.5 Recommendations for Future Work

The effects of the active fin and the roll motion’s effect on the overall flow

around the hull due to forward speed could be modeled using CFD. This would offer an

estimation of the actual flow field around the bilge keel, enabling a much better

understanding of what is happening, and a basis for calculating the lift component.

The highest measured loads occurred at the leading edge of the bilge keel. Taking

PIV measurements at the forward end of the bilge keel would yield flow measurements

where it has the most effect. Additionally, if the flow field measurement was expanded

to a SPIV configuration, the out of plane velocities would be directly measured. This

52

would improve upon the assumption that this velocity is constant across the span of the

bilge keel. If performed it would also help to quantify the force on the bilge keel due to

lift during the roll cycle.

Only the port bilge keel was gauged. The installed acquisition system could have

handled the extra channels, meaning only the cost of installing the gages and running

wire would be necessary. Understanding some of the unexpected force oscillations

would be aided by having matching data from the starboard bilge keel as well to compare

with.

Multiple options are available to help quantify the effects of the incoming wave

field on the bilge keel. A wave buoy collecting data in the test area would offer data on

the local wave heights and frequencies during the test. Multiple wave buoys would also

allow for the direction of the incoming waves. It would also be possible to measure the

wave field immediately in front of the vessel using optical and/or acoustic wave height

instrumentation currently in use at NSWCCD. If correlating to CFD models, free surface

height measurement directly above the bilge keel could be collected in the same manner.

53

LIST OF REFERENCES Atsavapranee, P., Carneal, J., Grant, D., Percival, A.S., “Experimental Investigation of Viscous Roll Damping on the DTMB Model 5617 Hull Form,” OMAE 2007-29324. Grant, D., Etebari, A., Atsavapranee P., “Experimental Investigation of Roll and Heave Excitation and Dampin in Beam Wave Fields,” OMAE 2007-29318. Silva, S.R., Pascoal, R., Rodrigues, B., Soares, C.G., “Forced Rolling Trials on Board a Portuguese Navy Frigate,” Marine Technology, Vol. 43, No. 3, July 2006. DeFatta, D. J., Lucas, J.G., Hodgkiss, W.S., Digital Signal Processing: A System Design Approach. John Wiley and Sons, New York, 1988.

Haddara, M.R., Zhang, S., “Effect of Forward Speed on the Roll Damping of Three Small Fishing Vessels,” Transactions of ASME, Vol. 116, May 1994. Himeno, Y., “Prediction of Ship Roll Damping-State of the Art,” Report 239, Department of Naval Architecture and Marine Engineering, University of Michigan, 1981. Ikeda, Y., Himeno, Y., Tanaka, N., “A Prediction Method for Ship Roll Damping,” Report 00405, Department of Naval Architecture, University of Osaka Prefecture, 1978. Keulegan, G.M. and Carpenter, L.H., “Forces on Cylinders and Plates in an Oscillating Fluid,” Journal of Research of the National Bureau of Standards, Vol. 60, 1958. Lloyd, A.R.J.M., Seakeeping: Ship Behaviour in Rough Weather, ARJM Lloyd, 1998. Lewandowski, E., The Dynamics of Marine Craft, World Scientific Publishing Company, 2004 Dalzell, J.F., “A Note on the Form of Ship Roll Damping,” Journal of Ship Research, Vol. 22, No. 3, Sept. 1978. Schmitke, R.T., “Ship Sway, Roll, and Yaw Motions in Oblique Seas,” SNAME Transactions, Vol. 86, 1978.

54

APPENDIX A – SHIP CHARACTERISTICS

55

Cur

ves

of F

orm

1000

.0

1100

.0

1200

.0

1300

.0

1400

.0

1500

.0

1600

.0

1700

.0

1800

.0 2.80

02.

900

3.00

03.

100

3.20

03.

300

3.40

03.

500

3.60

03.

700

Dra

ft (m

)

Volume (m3), Disp (tonnes)

600.

0

650.

0

700.

0

750.

0

800.

0

850.

0

900.

0

950.

0

1000

.0

1050

.0

Areas (m2)

Vol

ume

Dis

p (r

=1.0

25)

Wet

ted

Sur

face

Are

aW

ater

plan

e A

rea

56

Cur

ves

of F

orm

- C

ontin

ued

30.0

00

31.0

00

32.0

00

33.0

00

34.0

00

35.0

00

36.0

00

37.0

00

38.0

00

39.0

00

40.0

00 2.80

02.

900

3.00

03.

100

3.20

03.

300

3.40

03.

500

3.60

03.

700

Dra

ft (m

)

LCB (m), LCF (m), Moment (m-tonne)

0.00

0

1.00

0

2.00

0

3.00

0

4.00

0

5.00

0

6.00

0

7.00

0

8.00

0

VCB (m), KMT (m), Immersion (tonnes)

LCB

LCF

Mom

ent t

o Tr

im 1

cmV

CB

KM

TTo

nnes

/cm

Imm

ersi

on

57

Cur

ves

of F

orm

- C

ontin

ued

0.40

0

0.45

0

0.50

0

0.55

0

0.60

0

0.65

0

0.70

0

0.75

0

0.80

0 2.80

02.

900

3.00

03.

100

3.20

03.

300

3.40

03.

500

3.60

03.

700

Dra

ft (m

)

Coefficients

Cb

Cm

Cw

pC

pC

paft

Cpf

wd

58

Sect

iona

l Are

a C

urve

05101520253035

-10

010

2030

4050

6070

8090

Long

itudi

nal L

ocat

ion

(m fw

d of

AP)

Sectional Area (m2)

T =

2.88

0mT

= 3.

030m

T =

3.12

0mT

= 3.

240m

T =

3.36

0mT

= 3.

480m

T =

3.60

0m

59

APPENDIX B – RUN LOGS & CHANNEL ZEROS

60

TRIA

L LO

G F

OR

BET

TIC

A R

OLL

-DEC

AY

TEST

Run

#Sp

eed

over

Frou

de #

Dt

Dat

e/Ti

me

Ship

Win

d Sp

eed

Rol

l Per

iod

Seed

ing

Wat

erFi

ns C

ontr

olN

ote

# of

grou

nd (k

ts)

(ms)

Hea

ding

and

Dire

ctio

n(s

ec)

Tem

pR

elea

se (s

ec)

fram

es(k

ts, d

egre

es)

(deg

C)

252

0.0

0.00

0N

/A10

/03/

07, 2

141H

R20

Zero

run

for b

ores

ight

, rol

l bor

esig

ht s

et a

t -0.

353

253

7.5

0.13

82.

010

/03/

07, 2

204H

R20

Stea

dy s

tate

2000

256

7.5

0.13

81.

510

/03/

07, 2

218H

R20

Rol

l dec

ay, d

ata

colle

ct a

fter r

elea

se o

f fin

s co

ntro

l20

0025

77.

50.

138

1.5

10/0

3/07

, 230

7HR

20St

eady

sta

te20

0025

87.

50.

138

1.5

10/0

3/07

, 231

3HR

20R

oll d

ecay

, dat

a co

llect

afte

r rel

ease

of f

ins

cont

rol

2000

260

7.5

0.13

81.

510

/03/

07, 2

355H

R20

Stea

dy s

tate

2000

261

7.5

0.13

81.

520

24R

oll d

ecay

, dat

a co

llect

bef

ore

rele

ase

of fi

ns c

ontr

ol20

0026

210

.00.

184

1.0

10/0

4/07

, 005

4HR

20St

eady

sta

te20

0026

310

.00.

184

1.0

10/0

4/07

, 010

0HR

203

Rol

l dec

ay20

0026

410

.00.

184

1.0

10/0

4/07

, 013

4HR

20St

eady

sta

te20

0026

510

.00.

184

1.0

10/0

4/07

, 013

8HR

2031

Rol

l dec

ay20

0026

610

.00.

184

1.0

10/0

4/07

, 021

0HR

20St

eady

sta

te20

0026

710

.00.

184

1.0

10/0

4/07

, 021

5HR

2037

Rol

l dec

ay20

0026

810

.00.

184

1.0

10/0

4/07

, 024

5HR

20St

eady

sta

te20

0026

910

.00.

184

1.0

10/0

4/07

, 025

0HR

20Fo

rced

roll

only

, fin

s co

ntro

l was

not

rele

ased

2000

270

10.0

0.18

41.

010

/04/

07, 0

305H

R20

Rol

l Dec

ay20

00

Run

#Sp

eed

thru

Frou

de #

Dt

Dat

e/Ti

me

Ship

Win

d Sp

eed

Rol

l Per

iod

Seed

ing

Wat

erFi

ns C

ontr

olN

ote

# of

wat

er (k

ts)

(ms)

Hea

ding

and

Dire

ctio

n(s

ec)

Tem

pR

elea

se (s

ec)

fram

es(k

ts, d

egre

es)

(deg

C)

271

0.3

0.00

6N

/A10

/04/

07, 2

100H

R16

51,

13

no22

Zero

run

for r

oll/p

itch

bore

sigh

t, se

t at 0

.7, -

0.55

127

27.

50.

138

1.3

10/0

4/07

, 211

6HR

165

2, 3

02no

22St

eady

sta

te, c

ontr

ol fi

ns o

n au

to10

0027

37.

50.

138

1.3

10/0

4/07

, 212

2HR

165

2, 3

029.

55no

2288

Rol

l dec

ay (f

irst 3

20 fr

ames

bla

nk),

visu

al s

ea s

tate

020

0027

47.

40.

136

1.3

10/0

4/07

, 215

5HR

165

4, 1

03no

22St

eady

sta

te, a

uto

fins,

man

ual t

rigge

red,

zer

o at

1.2

kts

1000

275

7.4

0.13

61.

310

/04/

07, 2

201H

R16

54,

103

9.75

no22

40R

oll d

ecay

2000

276

10.5

0.19

31.

010

/04/

07, 2

237H

R16

62,

105

no22

Stea

dy s

tate

, con

trol

fins

on

auto

, zer

o ta

ken

at 0

.8 k

ts10

0027

710

.50.

193

1.0

10/0

4/07

, 224

2HR

166

2, 1

059.

65no

2216

Rol

l dec

ay20

0027

810

.00.

184

1.0

10/0

4/07

, 230

9HR

166

0, 2

6no

22St

eady

sta

te, c

ontr

ol fi

ns o

n au

to, z

ero

take

n at

0.7

kts

1000

279

10.0

0.18

41.

010

/04/

07, 2

317H

R16

60,

26

9.55

no22

20R

oll d

ecay

, fra

mes

85-

124

mis

sing

2000

280

10.7

0.19

71.

010

/04/

07, 2

343H

R16

62,

63

no22

Stea

dy s

tate

, con

trol

fins

on

auto

, zer

o ta

ken

at 0

.8 k

ts10

0028

110

.70.

197

1.0

10/0

4/07

, 234

9HR

166

2, 6

39.

55no

2214

Rol

l dec

ay20

0028

210

.00.

184

1.0

10/0

5/07

, 001

5HR

166

4, 3

26no

22St

eady

sta

te, c

ontr

ol fi

ns o

n au

to, z

ero

take

n at

0.6

kts

1000

283

10.0

0.18

41.

010

/05/

07, 0

020H

R16

64,

326

9.44

no22

43R

oll d

ecay

2000

284

7.0

0.12

91.

310

/05/

07, 0

103H

R16

66,

320

yes

22St

eady

sta

te, c

ontr

ol fi

ns o

n au

to, z

ero

take

n at

0.6

kts

1000

285

7.0

0.12

91.

310

/05/

07, 0

107H

R16

66,

320

9.90

yes

2214

2R

oll d

ecay

2000

286

7.4

0.13

61.

310

/05/

07, 0

135H

R16

69,

328

yes

22St

eady

sta

te, a

uto

fins,

vis

sea

sta

te 0

.1, z

ero

at 1

.0 k

t10

0028

77.

40.

136

1.3

10/0

5/07

, 014

0HR

166

9, 3

289.

70ye

s22

40R

oll d

ecay

2000

288

5.0

0.09

22.

010

/05/

07, 0

208H

R16

54,

345

yes

22St

eady

sta

te, c

ontr

ol fi

ns o

n au

to, z

ero

take

n at

0.4

kt

1000

290

5.1

0.09

42.

010

/05/

07, 0

237H

R16

64,

312

yes

22St

eady

sta

te, c

ontr

ol fi

ns o

n au

to, z

ero

take

n at

1.0

kt

1000

291

5.1

0.09

42.

010

/05/

07, 0

242H

R16

64,

312

9.25

yes

2225

Rol

l dec

ay20

0029

25.

00.

092

2.0

10/0

5/07

, 030

9HR

166

10, 3

45ye

s22

Stea

dy s

tate

, con

trol

fins

on

auto

, zer

o ta

ken

at 0

.6 k

t10

0029

35.

00.

092

2.0

10/0

5/07

, 031

5HR

166

10, 3

458.

90ye

s22

41R

oll d

ecay

2000

61

Run

#Sp

eed

thru

Frou

de #

Dt

Dat

e/Ti

me

Ship

Win

d Sp

eed

Rol

l Per

iod

Seed

ing

Wat

erFi

ns C

ontr

olN

ote

# of

sig.

wav

ew

ater

(kts

)(m

s)H

eadi

ngan

d D

irect

ion

(sec

)Te

mp

Rel

ease

(sec

)fr

ames

heig

ht (c

m)

(kts

, deg

rees

)(d

eg C

)29

40.

00.

000

2.0

10/0

8/07

, 220

0HR

150

18, 1

8no

21Ze

ro ru

n, b

ores

ight

set

at 0

.7, -

0.55

129

54.

80.

088

2.0

10/0

8/07

, 220

5HR

150

18, 1

8ye

s21

Stea

dy s

tate

, con

trol

fins

on

auto

, zer

o ta

ken

at 1

.2 k

t10

0013

296

4.8

0.08

82.

010

/08/

07, 2

212H

R15

018

, 18

yes

21R

oll d

ecay

2000

1329

74.

80.

088

2.0

10/0

8/07

, 221

6HR

150

18, 1

8ye

s21

Rol

l dec

ay, t

ried

agai

n20

0013

298

10.2

0.18

72.

010

/08/

07, 2

245H

R33

116

, 12

no21

Stea

dy s

tate

, con

trol

fins

on

auto

, zer

o ta

ken

at 1

.0 k

t10

0023

299

10.2

0.18

72.

010

/08/

07, 2

250H

R33

116

, 12

no21

14R

oll d

ecay

, hea

d se

a20

0023

300

10.3

0.18

92.

010

/08/

07, 2

321H

R15

011

, 355

no21

Stea

dy s

tate

, con

trol

fins

on

auto

, zer

o ta

ken

at 1

.0 k

t10

0022

301

10.3

0.18

91.

010

/08/

07, 2

325H

R15

011

,351

9.40

no21

21R

oll d

ecay

2000

2230

210

.10.

186

1.0

10/0

8/07

, 234

8HR

150

13, 3

49no

21St

eady

sta

te, c

ontr

ol fi

ns o

n au

to, z

ero

take

n at

1.1

kt

1000

1830

310

.10.

186

1.0

10/0

8/07

, 235

3HR

150

13, 3

49no

2123

Rol

l dec

ay, r

eally

goo

d im

ages

2000

1830

48.

30.

152

1.0

10/0

8/07

, 003

5HR

152

8, 3

59no

21St

eady

sta

te, c

ontr

ol fi

ns o

n au

to, z

ero

take

n at

1.0

kt

1000

1530

58.

30.

152

1.0

10/0

9/07

, 004

1HR

152

8, 3

59no

2143

Rol

l dec

ay20

0015

306

7.3

0.13

41.

310

/09/

07, 0

102H

R15

26,

347

no21

Stea

dy s

tate

, con

trol

fins

on

auto

, zer

o ta

ken

at 0

.9 k

t10

0020

307

7.3

0.13

41.

310

/09/

07, 0

107H

R15

26,

347

no21

105

Rol

l dec

ay20

0020

308

7.0

0.12

91.

310

/09/

07, 0

133H

R33

012

, 332

no21

Stea

dy s

tate

, con

trol

fins

on

auto

, zer

o ta

ken

at 0

.7 k

t10

0020

309

7.0

0.12

91.

310

/09/

07, 0

139H

R33

012

, 332

no21

47R

oll d

ecay

2000

2031

07.

00.

129

1.3

10/0

9/07

, 014

3HR

330

12, 3

32no

2113

0R

oll d

ecay

1000

2031

110

.10.

186

1.0

10/0

9/07

, 014

8HR

332

12, 3

17no

21St

eady

sta

te20

0020

312

10.1

0.18

61.

010

/09/

07, 0

154H

R33

212

, 317

no21

Rol

l dec

ay10

0020

Run

#Sp

eed

thru

Frou

de #

Dt

Dat

e/Ti

me

Ship

Win

d Sp

eed

Rol

l Per

iod

Seed

ing

Wat

erFi

ns C

ontr

olN

ote

# of

sig.

wav

ew

ater

(kts

)(m

s)H

eadi

ngan

d D

irect

ion

(sec

)Te

mp

Rel

ease

(sec

)fr

ames

heig

ht (c

m)

(kts

, deg

rees

)(d

eg C

)31

30.

00.

000

N/A

N/A

play

ing

arou

ndN

/A31

40.

00.

000

N/A

10/0

9/07

, 180

9HR

280

9, 1

78N

/A18

Zero

run,

bor

esig

ht s

et a

t 0.7

, -0.

551

N/A

1031

54.

80.

088

N/A

10/0

9/07

, 181

7HR

280

9, 1

78N

/A18

Stea

dy s

tate

, con

trol

fins

on

auto

, zer

o ta

ken

at 1

.0 k

tN

/A10

316

4.8

0.08

8N

/A10

/09/

07, 1

821H

R28

09,

178

N/A

188

Rol

l dec

ayN

/A10

317

4.8

0.08

8N

/A10

/09/

07, 1

825H

R28

09,

178

N/A

1850

Rol

l dec

ayN

/A10

318

4.8

0.08

8N

/A10

/09/

07, 1

829H

R28

09,

178

N/A

1843

Rol

l dec

ayN

/A10

319

4.8

0.08

8N

/A10

/09/

07, 1

836H

R28

09,

178

N/A

1843

Rol

l dec

ayN

/A10

320

7.5

0.13

81.

310

/09/

07, 2

112H

R21

114

, 216

no19

Stea

dy s

tate

, con

trol

fins

on

auto

, zer

o ta

ken

at 0

.5 k

t10

0011

321

7.5

0.13

81.

310

/09/

07, 2

119H

R21

114

, 216

no19

86R

oll d

ecay

2000

1132

27.

50.

138

1.3

10/0

9/07

, 212

3HR

211

14, 2

16no

1967

Rol

l dec

ay20

0011

323

7.5

0.13

81.

310

/09/

07, 2

127H

R21

114

, 216

no19

47R

oll d

ecay

2000

1132

47.

50.

138

1.3

10/0

9/07

, 213

1HR

211

14, 2

16no

1931

Rol

l dec

ay20

0011

325

10.3

0.18

91.

010

/09/

07, 2

155H

R27

26,

270

no19

Stea

dy s

tate

, con

trol

fins

on

auto

, zer

o ta

ken

at 0

.4 k

t10

0020

326

10.3

0.18

91.

010

/09/

07, 2

201H

R27

26,

270

no19

13R

oll d

ecay

2000

2032

710

.30.

189

1.0

10/0

9/07

, 220

4HR

272

6, 2

70no

1919

Rol

l dec

ay20

0020

328

10.3

0.18

91.

010

/09/

07, 2

208H

R27

26,

270

no19

19R

oll d

ecay

2000

2032

910

.30.

189

1.0

10/0

9/07

, 221

2HR

272

6, 2

70no

1920

Rol

l dec

ay20

0020

330

12.6

0.23

10.

810

/09/

07, 2

227H

R29

26,

327

no19

Stea

dy s

tate

, con

trol

fins

on

auto

, zer

o ta

ken

at 0

.3 k

t10

0024

331

12.6

0.23

10.

810

/09/

07, 2

233H

R29

26,

327

no19

5R

oll d

ecay

2000

2433

212

.60.

231

0.8

10/0

9/07

, 223

7HR

292

6, 3

27no

1917

Rol

l dec

ay20

0024

333

12.6

0.23

10.

810

/09/

07, 2

241H

R29

26,

327

no19

19R

oll d

ecay

2000

2433

412

.60.

231

0.8

10/0

9/07

, 224

5HR

292

6, 3

27no

1920

Rol

l dec

ay20

0024

335

12.0

0.22

00.

810

/10/

07, 0

053H

R18

08,

330

no19

Stea

dy s

tate

, con

trol

fins

on

auto

, zer

o ta

ken

at 0

.2 k

t20

009

336

12.0

0.22

00.

810

/10/

07, 0

059H

R18

08,

330

no19

18R

oll d

ecay

2000

933

712

.00.

220

0.8

10/1

0/07

, 010

4HR

180

8, 3

30no

1919

Rol

l dec

ay20

009

338

12.0

0.22

00.

810

/10/

07, 0

108H

R18

08,

330

no19

26R

oll d

ecay

2000

933

912

.00.

220

0.8

10/1

0/07

, 011

2HR

180

8, 3

30no

1948

Rol

l dec

ay20

009

340

15.3

0.28

10.

6510

/10/

07, 0

128H

R0

6, 3

40no

19St

eady

sta

te, c

ontr

ol fi

ns o

n au

to, z

ero

take

n at

0.3

kt

1000

934

115

.30.

281

0.65

10/1

0/07

, 013

4HR

06,

340

no19

33R

oll d

ecay

2000

934

215

.30.

281

0.65

10/1

0/07

, 013

8HR

06,

340

no19

21R

oll d

ecay

2000

934

315

.30.

281

0.65

10/1

0/07

, 014

1HR

06,

340

no19

12R

oll d

ecay

, cam

era

wen

t dea

d20

009

62

Run

#Sp

eed

thru

Frou

de #

Dt

Dat

e/Ti

me

Ship

Win

d Sp

eed

Rol

l Per

iod

Seed

ing

Wat

erFi

ns C

ontr

olN

ote

# of

sig.

wav

ew

ater

(kts

)(m

s)H

eadi

ngan

d D

irect

ion

(sec

)Te

mp

Rel

ease

(sec

)fr

ames

heig

ht (c

m)

(kts

, deg

rees

)(d

eg C

)34

40.

00.

000

N/A

10/1

0/07

, 221

3HR

166

8, 2

63N

/A21

Zero

run,

bor

esig

ht s

et a

t 0.7

, -0.

551

N/A

734

55.

00.

092

N/A

10/1

0/07

, 221

8HR

166

8, 2

63N

/A21

Stea

dy s

tate

, con

trol

fins

on

auto

, zer

o ta

ken

at 0

.8 k

tN

/A7

346

5.0

0.09

2N

/A10

/10/

07, 2

221H

R16

68,

263

N/A

2143

Rol

l dec

ayN

/A7

347

5.0

0.09

2N

/A10

/10/

07, 2

223H

R16

68,

263

N/A

2154

Rol

l dec

ayN

/A7

348

5.0

0.09

2N

/A10

/10/

07, 2

226H

R16

68,

263

N/A

2138

Rol

l dec

ayN

/A7

349

5.0

0.09

2N

/A10

/10/

07, 2

229H

R16

68,

263

N/A

2144

Rol

l dec

ayN

/A7

350

5.0

0.09

2N

/A10

/10/

07, 2

232H

R16

68,

263

N/A

2132

Rol

l dec

ayN

/A7

351

5.0

0.09

2N

/A10

/10/

07, 2

235H

R16

68,

263

N/A

2165

Rol

l dec

ayN

/A7

352

0.0

0.00

0N

/A10

/10/

07, 2

246H

R0

12, 2

78N

/A21

Zero

run,

bor

esig

ht s

et a

t 0.7

, -0.

551

N/A

2535

37.

40.

136

N/A

10/1

0/07

, 225

1HR

012

, 278

N/A

21St

eady

sta

te, c

ontr

ol fi

ns o

n au

to, z

ero

take

n at

0.6

kt

N/A

2535

47.

40.

136

N/A

10/1

0/07

, 225

5HR

012

, 278

N/A

2125

Rol

l dec

ayN

/A25

355

7.4

0.13

6N

/A10

/10/

07, 2

258H

R0

12, 2

78N

/A21

57R

oll d

ecay

N/A

2535

67.

40.

136

N/A

10/1

0/07

, 230

1HR

012

, 278

N/A

2144

Rol

l dec

ayN

/A25

357

7.4

0.13

6N

/A10

/10/

07, 2

303H

R0

12, 2

78N

/A21

40R

oll d

ecay

N/A

2535

87.

40.

136

N/A

10/1

0/07

, 230

6HR

012

, 278

N/A

2162

Rol

l dec

ayN

/A25

359

7.4

0.13

6N

/A10

/10/

07, 2

308H

R0

12, 2

78N

/A21

27R

oll d

ecay

N/A

2536

00.

00.

000

N/A

10/1

0/07

, 231

9HR

010

, 260

N/A

21Ze

ro ru

n, b

ores

ight

set

at 0

.7, -

0.55

1N

/A25

361

10.2

0.18

7N

/A10

/10/

07, 2

324H

R0

10, 2

60N

/A21

Stea

dy s

tate

, con

trol

fins

on

auto

, zer

o ta

ken

at 1

.2 k

tN

/A25

362

10.2

0.18

7N

/A10

/10/

07, 2

328H

R0

10, 2

60N

/A21

26R

oll d

ecay

N/A

2536

310

.20.

187

N/A

10/1

0/07

, 233

0HR

010

, 260

N/A

2118

Rol

l dec

ayN

/A25

364

10.2

0.18

7N

/A10

/10/

07, 2

333H

R0

10, 2

60N

/A21

16R

oll d

ecay

N/A

2536

510

.20.

187

N/A

10/1

0/07

, 233

6HR

010

, 260

N/A

2120

Rol

l dec

ayN

/A25

366

10.2

0.18

7N

/A10

/10/

07, 2

339H

R0

10, 2

60N

/A21

8R

oll d

ecay

N/A

2536

710

.20.

187

N/A

10/1

0/07

, 234

1HR

010

, 260

N/A

2119

Rol

l dec

ayN

/A25

368

0.0

0.00

0N

/A10

/10/

07, 2

350H

R0

14, 2

90N

/A21

Zero

run,

bor

esig

ht s

et a

t 0.7

, -0.

551

N/A

2536

912

.50.

230

N/A

10/1

0/07

, 235

8HR

014

, 290

N/A

21St

eady

sta

te, c

ontr

ol fi

ns o

n au

to, z

ero

take

n at

0.3

kt

N/A

2537

012

.50.

230

N/A

10/1

1/07

, 000

1HR

014

, 290

N/A

2117

Rol

l dec

ayN

/A25

371

12.5

0.23

0N

/A10

/11/

07, 0

004H

R0

14, 2

90N

/A21

16R

oll d

ecay

N/A

2537

212

.50.

230

N/A

10/1

1/07

, 000

7HR

014

, 290

N/A

2111

Rol

l dec

ayN

/A25

373

12.5

0.23

0N

/A10

/11/

07, 0

009H

R0

14, 2

90N

/A21

12R

oll d

ecay

N/A

2537

412

.50.

230

N/A

10/1

1/07

, 001

2HR

014

, 290

N/A

219

Rol

l dec

ayN

/A25

375

12.5

0.23

0N

/A10

/11/

07, 0

015H

R0

14, 2

90N

/A21

36R

oll d

ecay

N/A

2537

60.

00.

000

N/A

10/1

1/07

, 005

5HR

180

11, 2

83N

/A21

Zero

run,

bor

esig

ht s

et a

t 0.7

, -0.

551

N/A

837

715

.20.

279

N/A

10/1

1/07

, 010

1HR

180

11, 2

83N

/A21

Stea

dy s

tate

, con

trol

fins

on

auto

, zer

o ta

ken

at 1

.1 k

tN

/A8

378

15.2

0.27

9N

/A10

/11/

07, 0

104H

R18

011

, 283

N/A

2161

Rol

l dec

ayN

/A8

379

15.2

0.27

9N

/A10

/11/

07, 0

107H

R18

011

, 283

N/A

2113

Rol

l dec

ayN

/A8

380

15.2

0.27

9N

/A10

/11/

07, 0

109H

R18

011

, 283

N/A

2113

Rol

l dec

ayN

/A8

381

15.2

0.27

9N

/A10

/11/

07, 0

110H

R18

011

, 283

N/A

2115

Rol

l dec

ayN

/A8

382

15.2

0.27

9N

/A10

/11/

07, 0

112H

R18

011

, 283

N/A

2113

Rol

l dec

ayN

/A8

383

15.2

0.27

9N

/A10

/11/

07, 0

114H

R18

011

, 283

N/A

2113

Rol

l dec

ayN

/A8

63

Stra

in G

age

Zero

s

-1.5-1

-0.50

0.51 27

127

628

128

629

129

630

130

631

131

632

132

633

133

634

134

635

135

636

136

637

137

638

1

Run

Num

ber

Zero Voltage

BK

1B

K2

BK

3B

K4

BK

5B

K6

BK

7B

K8

BK

9

Day

2D

ay 5

Day

4D

ay 3

64

APPENDIX C – COMPLETE ROLL DAMPING FORCE PLOTS

65

APPENDIX D – ADDITIONAL PIV IMAGE SERIES

98

PIV Images at 5.0kts, Run 291 (t = 0,1,2,3,4,5s)

99


100


101

PIV Images at 7.5kts, Run 321 (t = 6,7,8,9,10,11s )

102


103


104


105


106


107


108

full scale investigation of bilge keel effectiveness at ... · the objective of this thesis is to...

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